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Explaining explain



Date: Sun, 01 Feb 1998 00:34:28 -0500
From: Bob Sciamanda <trebor@velocity.net>
Subject: Re: Explaining explain
. . . "truth" is a troublesome word we
can quite well do without when we talk about science. We should ban it
from any statements about science. . . .
-- Donald Simanek

I would also drop the word "theory" in favor of the word "model". The word
theory connotes a candidate for some absolute, objective "truth"; whereas a
model is used to convey useful information without the pretense of being
unique, complete or ultimate - in physics it is a useful way of describing
reality in human terms. This is the burden of paper of mine in Nov/Dec 1996
Quantum. It is reproduced @ http://www.edinboro.edu/~sciamanda/prelude.html

Bob
***********************************************************************

For the benefit of those who may not have access to the web I am posting
this article of Bob. I hope he will forgive me for doing this without his
explicit permission.
***********************************************************************
A Prelude to the Study of Physics

Author:
Robert J. Sciamanda, Edinboro University of Pennsylvania
sciamanda@edinboro.edu or trebor@velocity.net
This paper was first published in QUANTUM Vol 7 No 2, pg 45, Nov/Dec 1996

I. THEORIES AND MODELS

No physicist or engineer ever solves a real problem. Instead she creates a
model of the real problem and solves this model problem. This model must
satisfy two requirements: it must be simple enough to be solvable, and it
must be realistic enough to be useful; ie., it must be both conceptually
understandable and empirically fruitful.

The theories and "laws" of physics are also models. Whether in the solving
of a particular engineering problem or in the search for the wide ranging
laws of physics, the art of scientific analysis consists in the creation of
useful models of reality. The model is the interface between reality and the
human mind. As such, the model must be expressed in human terms; it is cast
in terms of concepts which we create from the data of our experience. Our
models speak as much about us, our experience and our modes of thought as
they do about the external reality being modeled.

I prefer to speak of models where others might speak of theories because the
word "model" emphasizes the criterion of usefulness. We tend to think of a
theory as a candidate for some absolute, objective truth; a model is used to
convey useful information without the pretense of being unique, complete or
ultimate. As an example of the conception, gestation, birth and growth of a
model in physics let us consider the history of the "ideal gas law" (PV=RT),
which you undoubtedly have studied in your chemistry classes.

II. THE HISTORY OF A MODEL

Despite the voluminous abstractions of ancient philosophers, no useful
understanding of gas behavior emerged throughout ancient history and the
middle ages. The possibility of a useful model awaited the creation of the
thermometer and the manometer. Each of these devices uses a thread of
mercury imbedded in glass in order to generate a number (the length of the
mercury thread) which varies in value as the device is subjected to varying
conditions. Boyle, Charles and Gay Lussac investigated the behavior of these
devices when connected to a gas under controlled conditions.

To collapse a very long story, their experimentation resulted in the
creation of the empirical relation PV = RT, the variables P and T
representing the readings of the manometer and thermometer respectively; R
is a constant for a fixed quantity of gas. If we then define P, V and T to
be measurements of properties of the gas, PV = RT becomes a useful model of
the gas behavior, even though P and T, at this point, have no deeper meaning
other than the numbers generated by the specified devices.

That there should exist any (let alone such a simple) relation among the
numbers generated by these (or any other) devices is not at all to be
expected; such serendipity can only be gratefully contemplated when it
appears. It is an instance of the profound meaning in one of Einstein's most
famous quotations: "The most incomprehensible thing about the world is that
it is comprehensible."

The creation of the model PV = RT was a giant leap forward; and note that
the crucial beginning step consisted in the free creation of a set of
concepts in terms of which meaningful questions might be put to nature so
that nature might respond in a meaningful way. These concepts are not lying
in nature awaiting discovery by some passive act of looking; they must be
actively created. This is how the properties of matter come to be. This is
how we define into existence those measurable properties of reality which we
find to be useful. They are human constructs in terms of which we might ask
meaningful questions, read nature's answers and organize our understanding
into useful and testable models.

Each of these concepts is quantitative in nature: the number generated by a
measuring device. Our empirical gas law is simply a relation (and very
useful) among the numbers (P,V,T) generated by our measuring devices; it is
an empirical model. The numbers generated by measuring devices have no
deeper meaning except within the context of a conceptual model of the system
being measured and its effect upon the measuring devices.

Boyle did his experimentation in the 1600's, while the pilgrims were
colonizing America. It was not until the mid 1800's, while Americans were
fighting over slavery, that Joule brought together the theories (models) of
Newtonian mechanics and atomism (then hotly contested) to create a
conceptual model of the ideal gas as a system of randomly moving point
particles. In this model P is quite naturally associated with the Newtonian
force concept and accounts for the behavior of the mercury manometer.
However there is no a priori mechanical association for the empirical
quantity T, the "temperature" of the gas as generated by the thermometer.

Herein lies a wonderfully simple instance of the incredibly awesome power of
an empirically based analytical science: the fruitful interaction of
experimental and theoretical physics. Newton's laws drove Joule's conceptual
model to a very illuminating result: the numerical value of the product PV
for Joule's gas is proportional to the total kinetic energy of the randomly
moving gas particles. Thus Joule's conceptual model bestows upon the
empirical temperature T, in PV = RT, a deeper meaning as a humanly invented
property of the gas; it becomes a measure of the energy of random motion of
the gas particles.

III. A MODEL OF MODELS

Thus it is that the mathematical model PV = RT has foundations as both an
empirical model and a conceptual model. I present it as a paradigm to
illustrate the properties of the model in physics:

1) It is a human construct, the offspring of both our experience and our
imagination.

2) It is quantitative and speaks of freely defined, measurable properties of
matter.

3) It has both an empirical and a conceptual usefulness: it presents a
testable numerical equality involving the numbers generated by specified
measuring devices, and it offers a conceptual framework for associating a
deeper meaning with these numbers.

4) The empirical usefulness of a model is a matter of experimental
verification, and once verified this usefulness will remain; future models
of a wider scope will include it as a special case.

5) The conceptual usefulness of a model can be a cultural matter, a matter
of institutional and personal taste (more of this later).

IV. CONCEPTUAL LIMITATIONS

Our conceptual models are of course produced from the data of our
experience. Every now and then I close my eyes and carefully feel an object
such as a piece of fruit, a table or my own face, and try to imagine what it
might be like to have never had the sense of sight. What sort of conceptual
models might I fashion as I explore reality using only the sense of touch?
(Try to form the concept of the shape of an object without invoking a visual
image.) How could I appreciate the language of a sighted person? There is no
way that a sighted person could convey to me his conscious experience of
light vs. darkness, let alone red vs. green. Our conceptual models could
communicate only through shaky analogies and metaphors, but our empirical
models could unambiguously communicate regarding the numbers generated by
measuring devices.

Conceptual models are observer dependent and observer limited. As the
physicist probes into the behavior of reality she strives to create
meaningful conceptual models of that reality, using as raw materials the
concepts fashioned from human experience. As she probes deeper she finds
that she has to become ever more creative and imaginative, generating
abstractions and cross fertilizations of her ideas in order to conceptually
model the behavior of reality in human terms.

There is no reason to expect that this process can be extended indefinitely.
It seems reasonable to anticipate that beyond a certain level of analysis
the behavior of reality cannot be conceptually modeled in literal human
terms, even though we may continue to be clever enough to create numerical
equalities involving the readings of our instruments. After all, our
instruments operate on the same superficial level as our senses.

We are already on the doorstep of this conceptual barrier. The mathematical
models of quantum theory defied even the imagination of Albert Einstein; he
was never able to conceive a satisfactory conceptual model of the reality
behind these equations. As regards creative "weirdness", modern art and
music are poor seconds to modern physics, even though the arts operate
completely free of any constraints, whereas physics operates under the
severe constraint of empirical usefulness!

V. STANDARDS, TASTE AND BEAUTY

Suppose that you are shipwrecked on a desert island and, with nothing better
to do, decide to create the science of physics from scratch. You decide that
your first task will be to choose (or design) standards for your
measurements of space and time intervals. How should you choose a standard
measuring rod and a standard clock? This is a "catch 22" question: one would
like to have these standards available a priori, so that one can perform
experiments (both physical and gedanken) to ask questions of nature, read
her answers and be guided toward a theory about the behavior of matter. Yet
one's choices of a standard clock and measuring rod already presuppose
considerable understanding about the behavior of matter! For example, the
choice of a standard clock already presupposes a theory which will be
committed to the conclusion that this particular mechanism ticks at a
constant rate. Logical consistency will force the theory to this conclusion.
Choices among theories and choices among standards are inextricably
intertwined.

The dilemma exposed in the above paragraph is not debilitating; we need only
replace the word "theory" (a candidate for an absolute, objective truth)
with the word "model" (a useful way of describing reality in human terms).
In this view, the choice of a clock simply defines into existence a
measurable parameter "t" which will be used as a linear time base for the
description of the evolution of phenomena. We will be comparing the course
of all other phenomena to the succession of ticks of this clock.

Clearly the choice of standards is a matter of free definition. The
criterion is not one of truth; it is simply one of usefulness: which choices
lead to the most "desirable" empirical and conceptual models of reality? Put
another way: how "weird" does the conceptual model have to get in order to
be empirically useful? The words "desirable" and "useful" must be defined by
you and/or current scientific culture; they are a matter of taste.
Historically, and logically, this is an iterative process, as we see more
and more details of where the model is leading.

Let me tease you with a famous example (which hopefully you will study in
detail later): Einstein, in his 1905 relativity theory, was the first to
capitalize upon this freedom of choice (of rods and clocks) in a radical
way. His definitions of "desirable" and "weird" were not mainstream. To him
the desirable model must preserve the invariance (sameness) of physical law
(in particular Maxwell's equations of electrodynamics) for all
non-accelerated observers. But conventional wisdom said that the velocities
appearing in Maxwell's equations must be measured from an absolute frame of
reference (the "aether" frame). This was "desirable" to many; they found it
satisfying that the laws of physics should be simple only to an observer at
absolute rest. In fact, any deviation of your experimental results from the
laws of physics would then furnish you with sufficient data to measure your
own absolute velocity. They had been disappointed that Newton's model of
mechanics did not allow us to measure our absolute velocity by mechanical
experiments (Newton himself must have been disappointed). They were
overjoyed that now Maxwell's model of electrodynamics (which includes light)
would allow us to measure our absolute velocity using optical experiments.

Einstein conceived a completely different conceptual model for Maxwell's
electrodynamics. He sought a model in which these equations could be used
with equal validity by all non-accelerated observers, each using the
numerical values of all quantities (eg., velocities) as measured from her
frame. He dared to redefine the measurement of space and time intervals to
make this so. It is to be expected that such a redefinition would force new
and worse weirdities into the model; we surely should expect that we will
have to design new clocks and measuring rods, with exotic "relativistic"
properties. The remarkable result has been that the new weirdities were only
cultural, that ordinary clocks and meter sticks behave relativisticaly, and
that a vast scope of phenomena have become more simply describable, even
phenomena far removed from Maxwell's equations. Widespread acceptance did
not come quickly or easily, but today relativity is not only accepted as
empirically and conceptually useful; it has become beautiful!

The search for beauty in our conceptual models has always been a driving
force and sometimes, as with Einstein's relativity, it seems to have been
the sole motivation. Today many, like Einstein, are disappointed in their
search for intuitive beauty in the quantum aspects of modern physics. Unlike
relativity, the beauty of quantum theory still eludes visceral human
appreciation. Perhaps with time we can acquire a taste, but it must begin
with an adjustment of our expectations, toward models rather than
"theories". Physics does not offer any quieting and ultimate answers.

VI. YOUR PERSONAL PHYSICS

Physics has not been idle; there is much for you to learn. To learn means to
make your own; it is an active process which only begins with listening and
reading. You must return often to listening and reading, but meaningful
learning comes only from contemplation. Each person must construct his own
models and his own philosophy of what physics is; these will grow and
develop; construction is never complete. What I have said here is subject to
criticism by scientists, philosophers, students and even myself, as my
appreciation of physics continues to develop. These words should be taken as
providing only a beginning for discussion and contemplation. I have tried to
express my current philosophy to you; over the years you will build your own
unique and personal version. Even more than the appreciation of a symphony
or painting, the understanding of physics is a unique and personal encounter
of a consciousness with reality.

-Bob Sciamanda, Edinboro Univ of PA